To extend a running distance of an inertia running mode and improve fuel consumption in a vehicle including a clutch separating an engine and wheels, it is conceivable that the vehicle is allowed to perform an inertia running mode with an engine brake force reduced when a predetermined condition is satisfied during normal running mode performed by using the power of the engine while the engine and the wheels are coupled. For example, in Patent Document 1, a control device of a vehicle is proposed that releases a clutch during running of the vehicle to separate an engine and wheels for performing the inertia running mode (referred to as neutral inertia running mode). In Patent Document 2, a control device of a vehicle is proposed that rests some of cylinders of the engine during running of the vehicle to reduce a pumping loss for performing the inertia running mode (referred to as cylinder resting inertia running mode).